Papers

Unsteady forces on spheres during free-surface water entry

Tadd T. Truscott^a1 c1, Brenden P. Epps^a2 and Alexandra H. Techet^a2

^a1 Brigham Young University, Provo, UT 84604, USA

^a2 Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Abstract

We present a study of the forces during free-surface water entry of spheres of varying masses, diameters, and surface treatments. Previous studies have shown that the formation of a subsurface air cavity by a falling sphere is conditional upon impact speed and surface treatment. This study focuses on the forces experienced by the sphere in both cavity-forming and non-cavity-forming cases. Unsteady force estimates require accurate determination of the deceleration for both high and low mass ratios, especially as inertial and hydrodynamic effects approach equality. Using high-speed imaging, high-speed particle image velocimetry, and numerical simulation, we examine the nature of the forces in each case. The effect of mass ratio is shown, where a lighter sphere undergoes larger decelerations and more dramatic trajectory changes. In the non-cavity-forming cases, the forces are modulated by the growth and shedding of a strong, ring-like vortex structure. In the cavity-forming cases, little vorticity is shed by the sphere, and the forces are modulated by the unsteady pressure required for the opening and closing of the air cavity. A data-driven boundary-element-type method is developed to accurately describe the unsteady forces using cavity shape data from experiments.

(Received April 21 2011)

(Reviewed April 11 2012)

(Accepted May 14 2012)

(Online publication July 02 2012)

Key Words:

• computational methods;
• free surface;
• vortex shedding

Correspondence:

^c1 Email address for correspondence: truscott@byu.edu